We planned to use a DA-modelling framework, similar to that used by Richardson et al. (2013) and Mahmud et al. (in preparation). This approach uses a simple carbon balance model shown in Figure 1. The model is driven by daily inputs of gross primary production (GPP). Total maintenance respiration (Rm,tot) is immediately subtracted, and the remainder enters a non-structural C pool (Cn). This pool is utilized for growth at a rate k. Of the utilization flux, a fraction Y is used in growth respiration (Rg), and the remaining fraction (1-Y) is allocated to structural C pools (Cs): among foliage, wood and root (Cs,f, Cs,w, Cs,r). The foliage and root pools are assumed to turn over with rate sf and sr respectively. We assume there is no wood turnover as evidenced from the experiment.
Figure 1: Structure of the Carbon Balance Model (CBM). Pools, shown as solid boxes: Cn, non-structural storage C; Cs,f, structural C in foliage; Cs,r, structural C in roots; Cs,w, structural C in wood. Dummy pools, shown as dashed boxes: Cf,lit, total C in foliage litterfall; Cr,lit, total C in root turnover. Fluxes, denoted by arrows, include: GPP, gross primary production; Rm,tot, maintenance respiration; Rg, growth respiration. Fluxes are governed by seven key parameters: k, storage utilization coefficient; Y, growth respiration fraction; af, allocation to foliage; aw, allocation to wood; \(a_r = (1-a_f-a_w)\), allocation to roots; sf, foliage turnover rate; sr, root turnover rate.
The dynamics of the four carbon pools (Cn, Cs,f, Cs,w, and Cs,r) are described by four difference equations:
\[\Delta C_n = GPP - R_{m,tot} - kC_n\] \[\Delta C_{s,f} = kC_n(1-Y)a_f - s_fC_{s,f}\] \[\Delta C_{s,w} = kC_n(1-Y)a_w\] \[\Delta C_{s,r} = kC_n(1-Y)(1-a_f-a_w) - s_rC_{s,r}\]
Where k is the storage utilization coefficient; Y is the growth respiration fraction; af, aw, ar are the allocation to foliage, wood and root respectively; sf and sr are the leaf and root turnover rates respectively; \(\sum s_fC_{s,f} = C_{f,lit}\) and \(\sum s_rC_{s,r} = C_{r,lit}\) are the dummy foliage and root litter pools respectively.
Total maintenance respiration, Rm,tot was calculated as a temperature-dependent respiration rates for foliage, wood and root (Rm,f, Rm,w and Rm,r respectively), multiplied by plant organ C masses (Ct,f, Ct,w, and Ct,r are the total C in foliage, wood and root respectively). Wood respiration was further partitioned into stem and branches. Similarly root respiration was partitioned into different root size classes (fine, intermediate, coarse and bole roots). Growth respiration (Rg) at each time step was calculated as a modeled respiration rate (Y) multiplied by plant biomass changes at that time step (\(\Delta C_{t,f} + \Delta C_{t,w} + \Delta C_{t,r}\)).
\[R_{m,tot} = R_{m,f} C_{t,f} + R_{m,w} C_{t,w} + R_{m,r}C_{t,r}\] \[R_{m,w} C_{t,w} = R_{m,s} C_{t,s} + R_{m,b} C_{t,b}\] \[R_{m,r} C_{t,r} = R_{m,fr} C_{t,fr} + R_{m,ir} C_{t,ir} + R_{m,cr} C_{t,cr} + R_{m,br} C_{t,br}\] \[R_g = Y(\Delta C_{t,f} + \Delta C_{t,w} + \Delta C_{t,r})\]
Where Rm,s, Rm,b, Rm,fr, Rm,ir, Rm,cr and Rm,br are the maintenance respiration rates with Ct,s, Ct,b, Ct,fr, Ct,ir, Ct,cr and Ct,br are the total C in stem, branches, fine roots, intermediate roots, coarse roots and bole roots respectively.
The non-structural (storage) C pool (Cn) is assumed to be divided among foliage, wood and root tissues (Cn,f, Cn,w, Cn,r) according to empirically-determined fractions.
- However, WTC-3 experiment only measured leaf non-structural C (Cn,f), and therefore to estimate the partitioning of the non-structural C among different organs, we hope to use data from WTC-4 experiment on similar-sized seedlings of a related species (Eucalyptus parramattensis). We will consider different treatments from the experimental dataset, to find the Cn partitioning to foliage, wood and roots.
- Another possibility (if WTC-4 data are not available!!) would be to assume another two parameters to estimate the Cn partitioning to foliage, wood and roots (pf, Cn partitioning to foliage; pw, Cn partitioning to wood; \(p_r = (1-p_f-p_w)\), Cn partitioning to roots).
Total carbon in each tissue (Ct) is then calculated as the sum of non-structural carbon (Cn) and structural carbon (Cs) for that tissue.
\[C_{t,f} = C_{n,f} + C_{s,f}\] \[C_{t,w} = C_{n,w} + C_{s,w}\] \[C_{t,r} = C_{n,r} + C_{s,r}\] We plan to estimate seven parameters (k, Y, af, aw, ar, sf, sr) of the CBM for this experiment using DA. GPP and maintenance respiration rates will be used as model inputs in the DA framework, whereas the measurements of total aboveground respiration (Rabove), total C masses (Ct,f, Ct,w, Ct,r), foliage litterfall (Cf,lit) and foliage NSC (Cn,f) will serve to constrain the parameters. Aboveground respiration (Rabove) was estimated by summing both maintenance and growth respiration components of foliage and wood.
\[R_{above} = R_{m,f} C_{t,f} + R_{m,w} C_{t,w} + Y\Delta C_{t,f} + Y\Delta C_{t,w}\]
Figure 2: Growth (Diameter) of Eucalyptus tereticornis trees exposed to warming and drought
It is obvious from Figure 1 that there were pre-existing differences between the warmed watered (black vs blue, Figure 1) and warmed drought (black vs pink, Figure 1) trees. It seems like the warmed-drought trees actually started the drought smaller than the warmed-watered trees (blue vs pink, Figure 1). If we go for the above option 2 (i.e. separate all 4 treatments from actual drought implementation on 12 Feb 2014), the diameter time series (red line, Figure 1) makes it look like there was a strong effect of the drought on the tree growth but it was more a function of pre-existing differences in tree size. The height data showed the similar pattern.
So based on both diameter and height data, we decided to represent drought and watered treatments separately from the beginning of the experiment. So total number of treatments = 4 (ambient+watered, ambient+droughted, elevated+watered, elevated+droughted) with sample size of n = 3 for each treatment.
c1 = 0.48 # (unit conversion from gDM to gC: 1 gDM = 0.48 gC)
Partitioning of the hourly net CO2 fluxes into the components of GPP and Rabove were done using a technique common to eddy-covariance research (Reichstein et al. 2005); described thoroughly in Drake et al. (2016, 2017-in preparation). We assumed GPP to be zero at night when PPFD = 0, indicating the measured net C flux in such conditions was used as the measure of Rabove. We utilized the direct measurements of whole-canopy Rabove and its temperature dependence at night to predict Rabove for each hourly measurement as a function of air temperature. We then calculated GPP as the sum of the measured net CO2 flux and the predicted Rabove, given the measured air temperature.
Figure 3: Daily GPP and aboveground respiration (Rabove) of Eucalyptus tereticornis trees for all 4 treatments. The grey bars represent standard errors for sample size, n=3.
Figure 4: Estimated biomass pool of WTC-3 Eucalyptus tereticornis trees for all 4 treatments. We predicted total C mass present in both foliage and wood with fortnightly interval, however only the initial and final C mass for roots. Note that, the points are jittered in all figures to see the grey standard error bars (n=3).
Litterfall was collected, dried, and weighed fortnightly for each tree. The dummy foliage litter pool, Cf,lit (g C) was estimated by cumulative summing of fortnightly litter starting from the flux measurements. The daily foliage litterfall was predicted as a linear function of time between two fortnightly consecutive measurements and will be used to constrain the parameter foliage turnover rate, sf.
Figure 5: Dummy leaf litterfall pool of WTC-3 Eucalyptus tereticornis trees for all 4 treatments. Note that, the points are jittered to see the grey standard error bars (n=3).
Figure 6: Foliage TNC pool, Cn,f over time of WTC-3 Eucalyptus tereticornis trees for all 4 treatments. Note that, the points are jittered to see the grey standard error bars (n=3).
Figure 7: Rootmass partitioning of WTC-3 Eucalyptus tereticornis trees for all 4 treatments. The grey shade shows the standard error (n=12).
Figure 8: The short-term temperature sensitivity of the respiration of individual leaves relative to leaf temperature. Error bars reflect the standard errors of Eucalyptus tereticornis trees exposed to each temperature treatments (n = 6).
Figure 9: Mass-based night-time leaf-scale dark respiration measured in Eucalyptus tereticornis at a set temperature of 25°C through time (first panel) and in relation to prevailing mean air temperature, Tair (rest of the panels). Mean values are those of replicate whole-tree chambers (n = 6 for ambient/warmed treatment), determined based on three individual leaf measures per chamber. No statistically significant variation for drought/watered treatment on leaf respiration.
Intermediate root respiration: For the intermediate size class of 2 to 10 mm, We interpolated respiration rates between the size classes to estimate the middle class using a simple log-log plot.
Figure 10: Daily mean respiration rates for all tree components (foliage, wood and roots). There were no statistically significant difference in respiration rates across drought/watered treatments. Both branch wood and coarse root respiration showed temperature acclimation having higher rates in ambient than warmed condition.
Hypothesis 1: NSC vs. Temperature - As Paul, Driscoll & Lawlor (1991) have shown, low T generally results in accumulation of carbohydrates, indicating that growth or storage are limiting. Conversely, at high temperatures, sink demand is large and assimilate is depleted so there should be a marked higher utilization rate (k).
- The carbohydrate concentration decreased in stem and root tissues for Citrus plants, while it increased in leaf tissues under moderate warm conditions (30/20ºC than at 25/20ºC, Ribeiro et al. 2012).
- We hypothesize that drought is carbon limiting and negatively impacts plant carbon balance and that plants will rely on stored carbon to survive carbon limitation and therefore deplete their stored carbon reserves over time.